Main points: Don't tighten spokes all the way the first time. Take bulges and dents out of rim and make rim round before tightening spokes. Easy to replace one or two spokes without taking wheel or tire off, except right rear. Problems you may have. All of this is dangerous.
Warning: Bending a rim to straighten it as I describe can weaken the rim, and can cause it to break which could cause injury or death. If you bend a rim, examine it after you bend it to see if it has any cracks in it. If it has a crack in it, do not put it on a bicycle because it could be dangerous. Also, spokes that have been under too much stress could break while someone is riding the bicycle causing a wreck, especially if more than one spoke breaks at the same time.
If the rim is not bent and ALL of the spokes need to be tightened, I have found that this is the best way to do it:
Don't tighten spokes with the tire aired up because the nipple may drill a hole in the rim liner and in the tube causing a flat. Let some air out of the tire before tightening spokes. Better still, take the tire off the rim to tighten spokes because you need to look at the nipples to see if any spokes are sticking up above the nipple. File off the part of the spoke that is sticking up above the nipple so it won't punch a hole in the tube.
Get a spoke wrench that almost EXACTLY fits the nipples. Check the width of several nipples because someone may have put in a spoke that has a different width nipple than the rest of the nipples. If you use a spoke wrench that is too large, you may round the corners of the nipples making it impossible to tighten the spokes with ANY spoke wrench.
Do this before tightening ANY spokes:
Use a large adjustable wrench to check the width of the rim everywhere to see if it has been bent in or bent out. Just put the jaws of the wrench so the rim will be between the jaws with the jaws barely touching both sides of the rim. Then move the wrench all around the rim and notice if the rim becomes narrower in some places, and too wide to pass between the jaws of the wrench in other places. If the sides of the rim has been bent in or out, you will need to bend it back to straighten it before you tighten spokes. If one or both sides of the rim is bent, there is a good chance that the rim is not round at the place where it is bent because the rider ran over a rock or something hit the rim. You can usually bend the rim back to make it straight without any special tools. See my guide on how to straighten bent rims.
If the rim is not the same width everywhere, the brakes may grab at the place where it is bent, or the tire could come off the rim while riding the bicycle. If the side of the rim has been bent inward, making the width of the rim narrower at that place, you can bend it back with a LARGE adjustable wrench. If you use a small wrench it will make a dent in the side of the rim. Get a flat piece of steel that comes just to the top of the lip of the rim and put it on the inside surface of the side of the rim. Put the jaws of the adjustable wrench so that the piece of steel and the side of the rim is between the jaws of the wrench. Pull the handle of the wrench bending the side of the rim back until it is straight. If you don't use a flat piece of steel, you can use the wrench only, but don't bend the rim much when you pull the handle of the wrench, and move the wrench a little after each pull. You will have to go over the entire length of the bend several times when you use the wrench only if it is a long bend.
To straighten outward bulges in the side of a rim, lay the rim on a flat piece of wood and hit the bulge with a hammer lightly, then hit it harder if needed. Use a hammer that will cover the entire bulge, not just the part of the bulge that is bent out most. Or, you can put the edge of a board on the bulge and hit the board with a hammer. Give plenty of support to the side that is not bent so it will not bend when you hit the other side with a hammer. If the side of the rim has a bulge, there is a good chance that the rim has been bent toward the hub by running over a rock or something, and the rim is no longer round. You can make it round again by bending it back. See my guide on bending rims to straighten them.
Check the rim to see if it is round (see if it is the same distance from the hub everywhere). This can be done in a few seconds by placing a yard stick on the hub and moving the yard stick around the hub. The rim may have high or low spots (places that are too far or too close to the hub) which would make you feel a "bump" as you ride the bicycle. If a rim is not round because it ran over a rock or ran into a tree, you will have to bend it back to make it round. But, if the rim is not round because it was cheaply made, or because someone tightened the spokes improperly, you can easily make it round in most cases by loosening spokes at the low places and tightening spokes at the high places.
To make the rim round when the rim is not actually bent, first TIGHTEN ALL SPOKES THE SAME AS IF THE RIM WAS ROUND. After you tighten all spokes, you can then correct the high and low places. Measure to find the distance that the rim needs to be from the hub. If there are places where the rim is too close to the hub, loosen the spokes in those places and loosen a few spokes on each end of those low places. Loosen more at the middle of the low place, gradually loosening a little less as you loosen spokes toward each end of the low place. Next, you can fix the high places if there are any. If there are places where the rim is too far from the hub, you can tighten spokes at those high places, tightening more at the middle of the high place and gradually tightening fewer turns as you tighten spokes toward the ends of those high places. Notice that you must first loosen spokes at the low places before you tighten spokes at the high places. Tightening spokes at the high places will help to make the low places go up to where they should be if you loosened spokes there first. If you have high places and no low places, you will need to loosen the spokes a little (maybe one-eighth turn) everywhere that is not a high place before you tighten spokes at the high places. If you have to tighten spokes too tight at a high place to make the high place round like the rest of the wheel, maybe you should loosen spokes a little at places that are not high places so you won't have to tighten spokes so tight at the high place.
Next, you can begin tightening all spokes.
If some nipples will not tighten because of corrosion on the threads of the spoke, first try to break the corrosion and free the nipple by LOOSENING the nipple because it won't be as hard to turn the nipple that way. If you find ONE nipple that will not tighten because of corrosion, stop and try ALL of the nipples to see if they will turn. Mark the spoke where you stopped so you will know where to start again after you loosen all of the corroded spoke nipples. When you turn a nipple to check it, turn the nipple back to the same position it was in before you turned it because you want to tighten ALL of the nipples the SAME NUMBER of turns when you start tightening them. The truing of the rim is done AFTER you have tightened all spokes.
If you have to replace any spoke, replace only ONE, and then tighten it only to the same degree of looseness as the rest of the spokes. Then, replace another spoke and tighten it only to the same degree of looseness as the other spokes. Repeat this procedure until you have replaced all of the spokes that need to be replaced. When you finish replacing all of the bad spokes, you are now ready to tighten ALL spokes.
DO NOT tighten each spoke until it is tight. DO NOT tighten each spoke all the way the first time around, and maybe not the second time around. If you tighten each spoke as tight as it needs to be the first time you tighten it, the hub will not be in the middle of the rim when you finish and the bicycle will go up and down when you ride it causing a very rough ride.
Before you start tightening spokes, mark the first spoke that you will tighten so you will know when you have PARTLY tightened all of the spokes in the wheel the first time. Tighten each spoke the SAME AMOUNT (same number of turns, not the same tightness). Tighten EACH spoke ONLY one-half turn. Or, tighten all spokes one-fouirth turn if most of the spokes are not very loose. If most of the spokes are very loose, you might tighten each spoke one full turn. IMPORTANT: The first spoke that you partly tighten should still be a little loose, and you should turn each nipple the SAME NUMBER OF TURNS.
After you partly tighten every spoke in the wheel the same number of turns of the nipple, check to see if the spokes are tight enough . The first spoke that you partly tightened and left a little loose will now be tighter than it was after you partly tightened it. Tightening spokes in one place in a wheel will also tighten the spokes that are 180 degrees from them. If ALL spokes still need to be tightened some more, start over and tighten ALL spoke nipples the same number of turns again. Tighten all nipples one-fourth turn, or tighten all nipples one-half turn, whichever you think is best. Do not try to tighten the spokes. Just turn the nipple on EACH spoke the same number of turns. Do not try to do anything to true the rim as you tighten all of the spokes one or two times or more. After MOST of the spokes are tight as they need to be, THEN you can tighten the spokes that were looser than the other spokes. Tighten those remaining spokes to about the same tightness as most of the other spokes that are tight enough.
If most of the spokes seem to be as tight as they need to be, but some spokes still need to be tightened, FIRST make a determination about whether the rim is actually bent or not. If you discover that the rim is bent, it would be better to bend it back until it is straight before you tighten spokes. If some of the spokes are loose and most of the spokes are tight, this may indicate that the rim has been bent and you need to bend it back to make it straight. If the rim is bent, you need to know that before you tighten ANY spokes so you can bend it back straight before tightening spokes.
If the rim is not bent or you have straightened the bends, you have made the wheel round if it had high or low places in it, and you have tightened all spokes so that all are approximately the same tightness, you can begin to true the rim laterally.
One reason for not trying to true a rear rim laterally while you are tightening the spokes is that if the wheel is dished, you don't want to mess up the dish if it dished correctly. The other reason is that it is just easier to true a rim laterally AFTER you have tightened all spokes IF the rim is not bent. Rear wheels that have a freewheel or cassette are dished so they will run in the middle of the frame and be aligned with the front wheel. The plane of the rim in a rear wheel is closer to the right hub flange than the left flange because the distance from the frame to the hub flange is greater on the right side than on the left side. The plane of the rim in a front wheel is the same distance from the left and right hub flange, so a front wheel does not need to be dished. If you need to correct an improper dish, you can do it after you have tightened all spokes as described above. To correct an improper dish in a wheel, loosen all of the spokes on one side of the wheel the same amount and tighten all spokes on the other side of the wheel the same amount. On the side you tighten, don't use as much turn of each nipple as you turned the nipples on the side you loosened. Then, if that isn't enough you can go back and turn each nipple a little more.
You do not need a truing stand to true a rim. Just put the wheel in a frame, tighten the nuts (first tighten bearings if there is too much play in them) and place some object on each side of the rim with white paper underneath and a light shining on the paper so you can easily see the gap between the rim and the object. Turn the wheel and look at the gap between the sides of the rim and the object to see if the width of the gap changes as the wheel turns. This can be dangerous. Do not let any children in the room. Do not let anyone get close enought to touch the wheel or where the spokes could hit them. Don't turn the wheel fast because someone could get their finger or clothing caught in the wheel. or the wheel could sling something into the eye of someone. There are many ways that someone can be hurt by a bicycle wheel that is turning.
You can true the rim from side to side by tightening or loosening spokes in places where the rim needs to move to one side or the other. If you want the rim to move to the right at a place where it is too far left, first loosen spokes on the left side at that place, loosening more at the middle of the place. If spokes on the left at that place are not tight, you don't need to loosen them first. Next, tighten spokes on the right of that place, tightening more at the MIDDLE of that place and tightening less as you tighten toward each end of that place.
After you finish tightening spokes and truing the rim, you want all of the spokes in the wheel to be the same tightness if the rim has not actually been bent. Sometimes when the rim has been bent only a little, people will tighten spokes at the bent place to make the rim true enough to not rub the brake shoes too much at the bent place. In that case, the spokes on one side of the bent place will need to be tighter than the other spokes in the wheel and the spokes on the other side of the bent place will need to be looser that the other spokes in the wheel. This is not a good situation. You should bend that place back to make it straight before tightening spokes if you have the time. Also when things are not done right, they can be dangerous causing injury or death to the rider or someone else.
You MAY be able to replace a broken or damaged spoke without taking the wheel or tire off.
First, measure to get the length you need. To measure the length of a spoke, measure from the center of the mushroom that is on one end of a spoke to the end of the threaded end, then subtract 0.5 mm (one-half millimeter). Or, measure the straight part of the spoke. If the spoke is in a wheel and tight, and the wheel is true and round, you can measure from the center of the mushroom to the point where the spoke goes in the hole in the rim.
After you tighten the spoke, the spoke should not quite go all the way through the end of the nipple. This will allow you to tighten the spoke perhaps years later after the spoke has stretched without the spoke going all the way through the nipple where you would need to file it off. If a spoke goes throught the nipple and sticks up some, you would need to file it off so it won't punch a hole in the tube.
If you have a broken spoke that is causing your wheel to warp to one side, you may be able to easily replace that spoke and make your wheel straight and true again. You may not even need to take the wheel or the tire off the bicycle. If the spoke is NOT on the same side as a freewheel, just let the air out of the tire and pull the rim liner up with a screwdriver so you can remove the old nipple. Then, put in a new nipple, put in a new spoke in the same direction throught the hole in the hub as the old spoke, and tighten the nipple.
You will need a spoke wrench that fits your spoke nipples. Spoke nipples are different widths on different wheels, even if the wheels are the same size. Spoke wrenches that fit only one size nipple will not fit other size nipples that are frequently found on bicycles. Even spoke wrenches that fit 8 different size nipples may not have a slot that fits the nipples on your bicycle precisely enought to avoid rounding the corners of the nipple when you tighten it.
Problems you may have when putting in spokes:
If your rim has been bent by something hitting the rim, you will need to bend the rim back straight before you put in spokes. You may be able to straighten a very small bend in a rim by tightening a spoke at the bend. A rim may look bent where there is a broken spoke, but not be actually bent and will straighten easily just by putting in a new spoke.
If your bicycle has a freewheel or cassette on the rear wheel, you will probably have to take the freewheel or cassette off in order to replace a spoke on that side. A special tool will be needed to take off a freewheel or cassette.
If you want to put in a spoke without taking the wheel or the tire off the bicycle, after you unscrew the old nipple, be careful to not let it fall somewhere inside the tire and be hard to find. If the old nipple falls somewhere in the tire and you don't get it out, it could cause a hole in the tube.
Don't turn a nipple to tighten it or loosen it with the tire aired up tightly because the turning action could cause a hole in the rim liner and in the tube. Also, after you tighten a spoke, you want to look at the nipple to see if the spoke has gone all the way throught the nipple, and will punch a hole in the tube if you don't file it off.